delhanty

Even if progress by AIs in proving conjectures lags, it seems likely that AIs collectively will, in the next few years, find counterexamples to nearly all the Erdős (and other) conjectures that are actually false and also provably false.

That means we will able to assume that nearly all the remaining conjectures are either true or undecidable.

Surely, that's good for folks who just want to know where the truth boundaries in mathematics lie.

It's obviously causing a lot of soul-searching amongst professional mathematicians.

Arguably, they should have given less weight for the last 100 years to Hardy's view in 'A Mathematician's Apology' [0]:

> It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done.

Rota takes a much more balanced view in 'Indiscrete Thoughts' [1].

"Problem Solvers" take Hardy's view:

> ... The mathematical concepts required to state mathematical problems are tacitly assumed to be eternal and immutable. Mathematical exposition is regarded as an inferior undertaking. ...

While for "theorizers":

> Mathematical exposition is considered a more difficult undertaking than mathematical research.

If professional mathematicians can reinvent themselves, there will be plenty of work left to do to explain the results of AIs to other humans.

There probably needs to be a new career path into professional pure mathematics other than doing novel research in a PhD.

[0] https://en.wikipedia.org/wiki/A_Mathematician%27s_Apology

[1] https://ncatlab.org/nlab/show/Gian-Carlo+Rota

https://ncatlab.org/nlab/show/Gian-Carlo+Rota

I just learnt that fact from Wikipedia's article on Mordel's conjecture (now Faltings' theorem), was curious whether the theorem could be strengthened to obtain a full proof of Fermat’s Last Theorem (FLT) that is genuinely different from the Taylor–Wiles proof (or its later variants) and so asked an AI (in this case Grok via Twitter).

Grok correctly told me "no it's not possible", but then surfaced (as an aside) a nice expository article on the Taylor–Wiles proof by Faltings from AMS notices in July 1995, which I thought I'd share here:

https://www.ams.org/notices/199507/faltings.pdf

https://www.boost.org/library/latest/graph/

https://www.boost.org/doc/libs/latest/libs/graph/doc/biconne...

Am I correct to suppose both are C++ implementations of Tarjan's algorithm?

Can you say how the it's similar and how it's different to superficially similar sounding work?

(1) https://github.com/linebender/vello , dual Apache/MIT, by Raph Levien et al

(2) https://sluglibrary.com/ , proprietary, by Eric Lengyel (Terathon)

Are you able to say what the relevant settings are? (I would like to be able to do that too ...)

There isn't a "solution" - you're looking at a life-long mitigation and management strategy that will not be "brief".

The time commitment typically goes up as one ages. I could spend 40 hours a week on nutrition, exercise and relaxation if I was trying to optimize for chronic pain reduction.

But then nothing else would get done.

Become a select customer of Shapr3D and their CEO István Csanády might send you one.

https://twitter.com/istvan_csanady/status/188829861216722566...

Edit: Unigraphics X SDRC became the system we know today as Siemens NX

It came out at the end of 2024 - these guys must all be around 80 by now.

https://news.ycombinator.com/item?id=43169194

The article came out at the end of 2024 ... these guys must all be around 80 by now.

Edit: Unigraphics X SDRC became the system we know today as Siemens NX

DCM then chooses one valid solution that it believes is "close" to initial supplied positions/directions/radii etc for the geometry.

Does the current add-in use AI at all?

What is your plan when, in the event of you getting some traction, Autodesk etc. copy you innovations into the main product?

As per my other comments [1][2], I worked on this area at D-Cubed and Solidworks from 1995 to 2002. Feel free to connect with me via twitter DM @delhanty [3].

[1] https://news.ycombinator.com/item?id=41440016

[2] https://news.ycombinator.com/item?id=41440150

[3] https://twitter.com/delhanty

Well those systems and pretty much all of the mechanical CAD industry is built upon D-Cubed's DCM, so I'd expect the behaviour to be the same.

If I was creating a new 3D CAD system from scratch now I'd probably license Parasolid eventually, but I'd pass on DCM.

I don't want to dump on D-Cubed and John Owen though. I have huge respect for him and the company he created. This is technical criticism with the benefit of hindsight.

This is always the problem with add-ins like this as a business - you're essentially doing free market research for the application vendor.

In my experience of building a sketcher at D-Cubed for a consultancy client (1995-2000) on top of D-Cubed's DCM, this is because DCM's curves (which are unbounded BTW) are not directed so that there are lots of erroneous solutions to attempting to constrain G1 chains of tangent bounded curves. For example the Apollonius Problem [1][2] of 3 tangent circles/lines has 2^3 = 8 solutions. IMO if John Owen had chosen directed curves for DCM then dragging configurations of tangent circles would be more stable.

I'll end with a quote from the Preface of Julian Lowell Coolidge's 1916 "A Treatise on the Circle and the Sphere" [3]:

> Among the cartesian theorems there is a sharp sub-division between those where the radius is looked upon as essentially signless and those where a positive or negative radius is allowed.

[1] https://mathworld.wolfram.com/ApolloniusProblem.html

[2] https://observablehq.com/@d3/apollonius-problem#

[3] https://en.wikipedia.org/wiki/A_Treatise_on_the_Circle_and_t...

True - I implemented the first Solidworks Autodimension sketch as a contractor around 2002 based upon earlier work that I'd done for a consultancy client at D-Cubed in the late 1990s. I'm sure it could be improved with AI and a large data set of sketches though.

> Solidworks tries to help with this in the form of cycling through what it thinks are the most likely constraints to remove and then re-solving the sketch. It's OK, but that sort of tool could be better.

I agree it could be better. The behavior with under-constrained sketches depends on D-Cubed's DCM, and I seem to recall they were rather floppy. It seems kind of ridiculous to make users jump through the hoops of making sketches fully constrained once they've added the constraints they care about.

Are there any more recently ex-Stripe folks here willing and able to comment on how Stripe's developer environment might have evolved since the OP left in 2019?

https://pubmed.ncbi.nlm.nih.gov/26219105/

I’m very slow and stiff in the mornings and I drink a lot of black coffee to mitigate that.

Then, late afternoon, perhaps 6 to hours later, I take my creatine monohydrate for the day just before my ocean swim.

  DOI: 10.1056/NEJMoa2309822
  Date: 2024-03-07
  Publication: N Engl J Med 2024
  Volume: 390
  Pages: 900-910

https://www.theguardian.com/environment/2024/mar/06/microsco...

which at least had a link to the original paper.

BACKGROUND

Microplastics and nanoplastics (MNPs) are emerging as a potential risk factor for cardiovascular disease in preclinical studies. Direct evidence that this risk extends to humans is lacking.

METHODS

We conducted a prospective, multicenter, observational study involving patients who were undergoing carotid endarterectomy for asymptomatic carotid artery disease. The excised carotid plaque specimens were analyzed for the presence of MNPs with the use of pyrolysis–gas chromatography–mass spectrometry, stable isotope analysis, and electron microscopy. Inflammatory biomarkers were assessed with enzyme-linked immunosorbent assay and immunohistochemical assay. The primary end point was a composite of myocardial infarction, stroke, or death from any cause among patients who had evidence of MNPs in plaque as compared with patients with plaque that showed no evidence of MNPs.

RESULTS

A total of 304 patients were enrolled in the study, and 257 completed a mean (±SD) follow-up of 33.7±6.9 months. Polyethylene was detected in carotid artery plaque of 150 patients (58.4%), with a mean level of 21.7±24.5 μg per milligram of plaque; 31 patients (12.1%) also had measurable amounts of polyvinyl chloride, with a mean level of 5.2±2.4 μg per milligram of plaque. Electron microscopy revealed visible, jagged-edged foreign particles among plaque macrophages and scattered in the external debris. Radiographic examination showed that some of these particles included chlorine. Patients in whom MNPs were detected within the atheroma were at higher risk for a primary end-point event than those in whom these substances were not detected (hazard ratio, 4.53; 95% confidence interval, 2.00 to 10.27; P<0.001).

CONCLUSIONS

In this study, patients with carotid artery plaque in which MNPs were detected had a higher risk of a composite of myocardial infarction, stroke, or death from any cause at 34 months of follow-up than those in whom MNPs were not detected. (Funded by Programmi di Ricerca Scientifica di Rilevante Interesse Nazionale and others; ClinicalTrials.gov number, NCT05900947. opens in new tab.)

That seems to concur with an informative article by AtaDistance from 2019 that I read the other day [0]:

> ...

> The result was InDesign 1.0 J which shipped in early 2001. InDesign J was the first, and only, major software application developed outside of Japan that followed the Japanese Industrial Standard (JIS) X4051 typesetting and composition specification (the kumihan “bible”) and traditional Japanese print production methods.

> I have covered some basics of Japanese layout before, but a review is helpful for first time readers. I’ll use a mix of my material and McCully’s presentation to explain.

> ...

> Western created DTP layout is graphics-driven and calculated by margins and font baselines. The western baseline typography model and font metrics is how PostScript and OpenType fonts, and all layout engines evolved. Adobe was well acquainted with the shortcomings of their own font technology and InDesign J got around the problems by adding proprietary Kanji virtual body font metrics and Japanese line break algorithms. None of this exists as an open standard that benefits everybody.

> That is fine for InDesign and print production, but web layout and typography via CSS is an entirely different world. There are 3 huge obstacles for good vertical Japanese typography on the web:

> * No font metrics for virtual body/em-box glyph space placement: everything has to be accomplished with baseline metrics

> * No reliable space control

> * No reliable line breaks

[0] https://atadistance.net/2019/04/26/the-state-of-css-japanese...

IIRC, ar5iv was created on his own initiative by Deynan Ginev

https://twitter.com/dginev/status/1736792316675825981

and it seems that he has worked tirelessly to fix nearly all of the edge cases during the collaboration.

This project creates huge value to humanity so Deynan is to be heartily thanked.

Does that include the C preprocessor?

Somehow, I recall someone here (maybe it was user walterbright) suggesting that implementing a C preprocessor was a lot of work - maybe months - so one might consider using Facebook's MIT licensed preprocessor:

https://github.com/facebookresearch/CParser

I don’t have an opinion on whether mobile phone usage is more or less likely to cause cancer than working in a radio station.

That is, wouldn’t we want to compare the radiant flux rather than the power?